Gait speed and individual characteristics are related to specific gait metrics in neurotypical adults

Gait biofeedback is a well-studied strategy to reduce gait impairments such as propulsion deficits or asymmetric step lengths. With biofeedback, participants alter their walking to reach the desired magnitude of a specific parameter (the biofeedback target) with each step. Biofeedback of anterior ground reaction force and step length is commonly used in post-stroke gait training as these variables are associated with self-selected gait speed, fall risk, and the energy cost of walking. However, biofeedback targets are often set as a function of an individual’s baseline walking pattern, which may not reflect the ideal magnitude of that gait parameter. Here we developed prediction models based on speed, leg length, mass, sex, and age to predict anterior ground reaction force and step length of neurotypical adults as a possible method for personalized biofeedback. Prediction of these values on an independent dataset demonstrated strong agreement with actual values, indicating that neurotypical anterior ground reaction forces can be estimated from an individual’s leg length, mass, and gait speed, and step lengths can be estimated from individual’s leg length, mass, age, sex, and gait speed. Unlike approaches that rely on an individual’s baseline gait, this approach provides a standardized method to personalize gait biofeedback targets based on the walking patterns exhibited by neurotypical individuals with similar characteristics walking at similar speeds without the risk of over- or underestimating the ideal values that could limit feedback-mediated reductions in gait impairments.

Gait training is a common component of rehabilitation paradigms for individuals with gait dysfunction secondary to musculoskeletal and neurological conditions. This training typically involves interventions that target stability, endurance, speed, and movement patterns during walking [1][2][3][4][5] . In this context, clinicians often provide external cues or feedback to change different aspects of walking that are associated with gait speed 6,7 , fall risk 8-10 , orthopedic injury 11,12 , and metabolic cost 6,10,13,14 in many patient populations. This has prompted research studies designed to evaluate the use of real-time biofeedback to change gait biomechanics.
These studies have largely focused on the effects of visual gait biofeedback, with kinematic and kinetic gait variables most often fed back to the learners 15 . In studies of gait dysfunction post-stroke, for example, visual biofeedback is often used to promote increases in step length (and reductions in step length asymmetry) [16][17][18][19] or increases in peak anterior ground reaction force 20,21 . These gait biofeedback variables are also common targets in studies of gait in older adults 22,23 and individuals with Parkinson's Disease 24,25 .
However, recent literature reviews have highlighted that the results across studies of gait biofeedback are inconsistent (for review see van Gelder, et al. 2018 15 and Spencer, et al. 2021 26 ); due, in part, to methodological heterogeneity. They found that studies differ in the modality of the biofeedback provided and the gait variable fed back to the learner. Even between studies that are matched for these factors, the methods to set the target values for biofeedback schemes vary.
Step length biofeedback targets for people post-stroke have been set in a variety of ways. Some studies ask participants to lengthen their shorter step to the length of their longer step 18,19 , while others instruct participants to make the right and left step lengths equal by setting the target to be the average of the two step lengths 27 or without any direction on which step length they should change 28,29 . Anterior Scientific Reports | (2023) 13:8069 | https://doi.org/10.1038/s41598-023-35317-y www.nature.com/scientificreports/ ground reaction force biofeedback targets are often set as a percent increase from baseline walking values, but the magnitude of this increase varies between studies 22,30 . The methodological variability in biofeedback target setting reflects our limited understanding of the desired target magnitudes for these metrics. While there seems to be broad agreement that the targets should be individualized, this is currently achieved by setting biofeedback targets as a function of an individual's baseline walking pattern. However, this may over-or underestimate the true desired target values for these metrics, and there is currently no way to determine a priori if this method of target setting is appropriate or accurate. One viable approach may be to understand the magnitudes of step length and anterior ground reaction force exhibited by neurotypical individuals of similar ages and body morphologies, walking at similar speeds.
Here, we built prediction models for peak anterior ground reaction force and step length of neurotypical adults using individual characteristics and gait speed. Then, we evaluated if these models could be used to predict the anterior ground reaction forces and step lengths of neurotypical adults in an independent dataset. We also compare the performance of this prediction model to the performance of age-and sex-based norms reported for peak anterior ground reaction force 31 and step length 32 . We hypothesized that predicting peak anterior ground reaction force and step length using our prediction equations (that include leg length, mass, age, sex, and gait speed) would allow for an accurate individualized estimation of these gait metrics beyond that provided by ageand sex-based norms. This work will provide the framework for a more standard methodology to personalize biofeedback targets in gait rehabilitation research.

Results
In this study, we completed a secondary analysis of two previously collected gait datasets to create models based on speed, leg length, mass, sex, and age to predict peak anterior ground reaction force and step length of neurotypical adults. These models were then validated on an independent dataset and compared to the accuracy of normative values for those individuals. Speed was included in the models given its known relationship with peak anterior ground reaction force and step length 33 . Leg length was included as a proxy for height, given that step length scales with height 34 and height was not reported in the independent dataset. Mass was included because ground reaction forces scale with mass 34 . Biological sex was included secondary to normative data that suggests an effect of sex on step lengths 32 . Age was also included given the evidence that step length and anterior ground reaction forces change with age [35][36][37][38] . One dataset was used to train the models (a training dataset) and the other to validate them (an independent validation dataset).
Model selection. Best subset model selection was used to identify the best models for the training dataset.
The final step of the model selection process for peak anterior ground reaction force is shown in Table 1 and for step length in Table 2. The model with the lowest Akaike information criterion (AIC) was selected as the final prediction model for each variable.
Prediction of peak anterior ground reaction force magnitude. The model that best predicted peak anterior ground reaction force (AGRF) magnitude included fixed effects for speed, speed 2 , mass, and leg length, as well as a random slope (speed) and intercept. Figure 1A displays examples of individual model fits for the training data. Figure 1B shows the mean fixed-effects model displayed against individual training data. The nonstandardized and standardized beta weights for each predictor in the peak anterior ground reaction force model are provided in Table 3. The standardized beta weights indicate that the primary predictor of peak anterior ground reaction force in neurotypical gait is gait speed. Predictions from this model of peak anterior ground reaction force showed strong agreement with the actual values of peak anterior ground reaction force magnitude in an independent dataset (N = 22; Fig. 2; R 2 relative to the unity line = 0.76). These predictions had an RMSE = 15.98 N. Furthermore, relative to the actual values of peak anterior ground reaction force, predictions from this model had a significantly smaller mean absolute error (2.1 ± 1.8) than normative values (7.2 ± 4.2; p = 7.00E-6).   Specifically, we created a vector of 20 speeds ranging from the minimum to the maximum speeds and found the age, mass, and leg length group means. These simulated values were used with the fixedeffects only model (for men, as sex was coded in the model as male = 0) to calculate predicted values that are plotted in blue. Individual data are plotted on a color spectrum from light orange to dark brown to represent participant mass as a third dimension of the data. Table 3. Non-standardized betas and standardized beta weights for the peak anterior ground reaction force model. The coefficients for each independent variable (and intercept) in the model are displayed in order of the absolute magnitude of the standardized beta weight. sex, and leg length as well as a random slope (speed) and intercept best-predicted step length (SL) magnitude. Example individual model fits on training data are displayed in Fig. 3A, and the mean fixed-effects model against all individual training data are in Fig. 3B. The non-standardized and standardized beta weights for each predictor in the step length model are provided in Table 4. The standardized beta weights of this model indicate that the primary predictor of neurotypical step length is gait speed. Predictions from this model of step length showed moderate agreement with the actual values of step length magnitude within the full independent dataset (N = 22; Fig. 4a; (R 2 relative to the unity line = 0.70). These predictions had an RMSE = 0.07 m. Of note, the model overestimated the actual step lengths that were < 0.31 m, which were not represented in the training dataset.  Spreadsheets to calculate the predicted magnitudes of peak anterior ground reaction force and step length for an individual are provided in the Supplementary Material S1.

Discussion
In this study, we developed models to predict the magnitudes of peak anterior ground reaction force and step length observed in neurotypical individuals while walking at different speeds. Both models accounted for the individual's gait speed, mass, and leg length, while the prediction model for step length also included terms for age and sex. We then tested the performance of these prediction models on an independent dataset. The modelpredicted magnitudes of peak anterior ground reaction force and step length were in strong and moderate agreement with the actual values of these measures, respectively. Moreover, the model-predicted magnitudes for both parameters were more accurate than age-and sex-based norms (demonstrated by smaller mean absolute errors). This suggests that these prediction models can generate reasonable estimates of individualized reference values for peak anterior ground reaction force and step length during walking at a wide range of gait speeds. This has important implications for gait rehabilitation research or clinical gait training-the model equations can be used to calculate peak anterior ground reaction force and step length magnitudes that reflect a premorbid, Table 4. Non-standardized betas and standardized beta weights for the step length model. The coefficients for each independent variable (and intercept) in the model are displayed in order of the absolute magnitude of the standardized beta weight.  www.nature.com/scientificreports/ non-pathological walking pattern given someone's gait speed and a few individual characteristics that are easily collected. Very few studies have investigated the prediction of neurotypical gait parameters. Most of these studies have developed methods to predict lower extremity joint angles and moments at different gait speeds [39][40][41][42] ; which, compared to step length and peak anterior ground reaction force, are not often the focus of research or clinical interventions. While no prior work has predicted peak anterior ground reaction force observed during neurotypical gait, one study has attempted to predict the step lengths of neurotypical adults using age, height, body impedance, and muscle activity. 43 Unfortunately, it is difficult to compare the performance of this model to the step length model reported here, as the model from Park, et al. was not validated on an independent dataset and our dataset does not have body impedance or muscle activity measures.
One could argue that age-and sex-based normative values for peak anterior ground reaction force 31 and step length 32 could be used to estimate the ideal magnitude of these parameters for an individual with gait dysfunction instead of employing more complicated prediction models like those developed here. However, age-and sexbased values for different gait parameters have limited generalizability to clinical populations as they are reported for gait speeds that are higher than typically observed in a clinical population. For example, in the "slow gait" condition tested in Öberg, et al. 1993, men between the ages of 50-59 walked at an average speed of 0.86 m/s. While this may be useful information for some, it does not allow for an accurate estimation of normative gait parameters for an individual that is not walking at a normative gait speed (e.g., a man who is 56 that is walking at 0.65 m/s following a stroke). This point is supported by the significant differences between the absolute error of the normative and predicted data observed here as well as the value of gait speed in the predictions indicated by the standardized beta weights (Tables 3 and 4). As such, the prediction models developed in this study make a unique contribution to this area of research by (1) providing a means to estimate the neurotypical magnitude of two clinically-relevant gait parameters at a wider range of speeds with greater accuracy than has been reported before and (2) validating these predictions on an independent data set.
One important implication of the prediction models developed in this study is that predicted peak anterior ground reaction force and step length values can be evaluated relative to the actual values in a population with gait dysfunction. These can then be used to determine the presence and magnitude of gait pattern deficits-without the need for demographically-and speed-matched neurotypical control data. This may significantly reduce the data collection burden for research studies and help inform clinical decision-making.
The ability to generate individualized reference values for peak anterior ground reaction force and step length provides a promising standard methodology to inform individualized gait biofeedback targets. To date, biofeedback targets for anterior ground reaction force and step length have largely been anchored to baseline walking patterns 18,22 . This is largely because targets anchored to baseline behavior are individualized and assumed to be achievable. However, it is possible that this approach generates target values that over-or underestimate the ideal target value. In cases where individuals have low baseline values for step length and anterior ground reaction force, this approach could mask additional capacity for change in movement patterns. We posit that using the values predicted from neurotypical gait behavior as a benchmark for the ideal target value would reduce the risk of masking someone's capacity for change in studies of gait biofeedback. Though future work is necessary to determine the most appropriate way to implement the use of biofeedback targets based on neurotypical gait behavior to ensure the movement goals are still attainable, particularly if the magnitudes are much higher than baseline walking values.
Although we suggest the use of neurotypical gait behavior as a point of reference, we acknowledge that there is currently no consensus in the field on the "ideal" gait pattern for individuals within a given patient population. For example, people with Parkinson's Disease generally benefit from feedback to increase their step lengths, but the exact step length magnitude that would optimize multiple aspects of walking (e.g., energy expenditure, dynamic balance, gait speed) for each person is poorly understood. With this work, we are assuming that the gait parameters of a neurotypical person with the same demographic characteristics walking at the same speed are a reasonable estimation of the "ideal" parameter values. While this logic may eventually be refuted with data as our understanding of optimal gait patterns in clinical populations with gait dysfunction evolve, there is currently no evidence to suggest that this approach is inherently flawed.
There are a few limitations to this study. First, the models are trained to predict a specific range of peak anterior ground reaction force and step length values and predictions outside of this range will be less accurate-as demonstrated by the larger RMSE of the step length predictions from the full independent validation dataset compared to that from the subset of data within the training set range. In addition to this, the models were trained on data with a specific range of anthropomorphic characteristics (age: 21-71 years; leg length: 0.65-0.91 m; mass: 45-95 kg), and the predictions may be less accurate for individuals who are outside these ranges. We also intentionally focused on predicting the gait metrics that are commonly studied and targeted with biofeedback in neurologic patient populations. However, other metrics may be of more interest or relevance in other diagnoses or gait pathologies (e.g., stance time asymmetry in individuals with lower extremity amputations 44 ). Furthermore, we chose to use training data from participants that were not walking with the use of handrails which may limit the generalizability of these findings to clinical populations that often require the use of handrails for treadmill walking. This decision was made because the original training dataset only included four participants that used handrails while walking, which is not enough data to reliably evaluate the effect of handrail use on these gait parameters. Future work is necessary to assess the effect of using handrails on these gait parameter estimations. Finally, we did not test how well these equations can be generalized to overground walking though prior work suggests people walk with similar kinematic and kinetic metrics to those examined here during both treadmill and overground walking 45 .
In conclusion, we developed prediction models for peak anterior ground reaction force and step length that demonstrated strong agreement when validated on an independent dataset and better accuracy than normative www.nature.com/scientificreports/ data. The best prediction models included terms that captured gait speed and demographic characteristics (i.e., age, mass, leg length, sex). These models (and the associated calculation tables provided in the supplementary material S1) can be used to create individualized reference values of peak anterior ground reaction force and step length for use in gait rehabilitation research and clinical practice.

Methods
Training dataset. To train the prediction models, we used a publicly available dataset of 42 neurotypical adults walking on a treadmill at eight different speeds, ranging from 40 to 145% of their self-selected speed (mean of self-selected comfortable gait speeds: 1.25 ± 0.16 m/s; range of comfortable gait speeds: 0.89-1.54 m/s; total range of gait speeds: 0.36-2.23 m/s) 46 . At each speed, participants walked for 90 s, and data from the last 30 s of each trial were used in this analysis to allow the participant to adjust to each speed before recording their data. Kinematic data were recorded at 150 Hz and kinetic data at 300 Hz. To ensure accurate kinetic data, the data from four participants in the original dataset who used treadmill handrails while walking were removed. Another participant from this dataset was removed due to an aberrant offset in the force data. Therefore, we trained the models with data from a total of 37 neurotypical adults (age: 40 ± 17 years (21-71 years); leg length: 0.78 ± 0.07 m (0.65-0.91 m); mass: 67 ± 12 kg (45-95 kg) and sex (coded as male = 0 and female = 1)). For ten of the 37 participants, data from only six or seven (out of eight) trials were included in the analysis. Six of these participants were unable to complete the fastest walking speed. In the other four cases, the participants completed all walking trials, but we excluded the data from the trials in which the participants drifted across the midline of the instrumented treadmill (i.e., stepped on both the right and left force plates simultaneously). We were able to use the remaining data from these participants in our analysis because the statistical approach we employed (described below) is robust to missing data. To account for the influence of other individual characteristics on peak anterior ground reaction force and step length, we extracted each participant's age, leg length, sex, and mass. We defined leg length as the vertical distance from the greater trochanter marker to the lateral malleolus marker while the participant stood upright. Please see the previous publications 46,47 for additional information about the data collection procedures.

Independent validation dataset.
Normative peak anterior ground reaction force and step length data. To compare the performance of our model to previously published age-and sex-based norms, we extracted the normative peak anterior ground reaction force and step length values for each participant in the independent validation set. Normative values for peak anterior ground reaction force were obtained from Chao et al. 31 , which reports normative values for both men and women across a large age range. The normative peak anterior ground reaction force value for each participant was selected by the age and sex of each participant. Because these data were only reported for a narrow range of speeds (0.63-0.76 m/s), most of the normative estimates could not be speed-matched. Normative values for step length were obtained from Öberg, et al. 32 because this paper reports normative data for men and women between the ages of 10-80 at three different gait speeds. The normative step length value for each participant was selected primarily based on age, sex, and the closest possible gait speed.
Data processing. For both datasets, we analyzed the kinematic and kinetic data from the right lower extremity using MATLAB R2021a. Data from the left leg was not included in the analysis as the step length and anterior ground reaction force values on the right and left sides were highly correlated. For both datasets 46,47 , kinematic data were lowpass filtered with a cutoff frequency of 6 Hz 48 , while kinetic, at 20 Hz 47 . Vertical ground reaction forces were then used to identify kinetic gait events. Heel strike was identified at the point when vertical ground reaction force reached 100 N and toe-off at less than 100 N.
We defined peak anterior ground reaction force as the maximum anterior ground reaction force between heel strike and toe-off. The average peak anterior ground reaction force over each 30-s trial was used for all analyses.
Step length was defined as the fore-aft difference between the right and left lateral malleoli markers at heel strike. The average step length over each 30-s trial was used for all analyses.
Statistical analyses. We used linear mixed-effects models to determine if peak anterior ground reaction force and step length magnitudes were associated with speed (m/s), mass (kg), leg length (m), sex, and age (years). Given the known relationship between gait speed and both peak anterior ground force and step length 33 , the minimum model included a fixed effect for speed. Because visual inspection of the data indicated a nonlinear relationship between speed and peak anterior ground reaction force and step length, we also considered models with a quadratic transformation of speed. In addition to these fixed effects, we included both a random intercept and a random slope for speed to account for repeated measures and between-subjects variability. The best subset model selection approach was used to identify the best model in the training data set. Best subset selection was performed by first comparing all possible models with the same number of variables and selecting the one with the highest adjusted R 2 value to yield a candidate set of seven models 49 . Then models with different numbers of parameters were compared using the Akaike information criterion (AIC) and the model with www.nature.com/scientificreports/ the lowest AIC was selected as the final prediction model. This process was completed independently for peak anterior ground reaction force and step length. We checked for linearity, multicollinearity, outliers, and influential points for both peak anterior ground reaction force and step length prediction models. The residuals vs fitted plots showed that, for the best models, there was no deviation from linearity. The variance inflation factors (VIF) for each of the coefficients were less than 5, indicating no major issues with collinearity. We identified one significantly influential point (one walking speed for a single participant) in the peak anterior ground reaction force model using Cook's distance at a threshold of 0.11. We removed this influential point (0.3% of the total number of data points) and refit the final peak anterior ground reaction force model. Unlike for inference, the normality and homoscedasticity assumptions of linear mixed-effects modeling do not need to be met for prediction. For the same reason, we did not select the predictors based on p-values, as the best subset model selection process determines the model that provides the best prediction versus determining which predictors are most important 49 .
To understand the relative value of each variable in the prediction models, we determined the standardized beta weights for each variable. To do this, we first calculated the z-score for peak anterior ground reaction force, step length, and the continuous predictors to standardize them. Sex is a categorical variable, so it did not need to be standardized for this analysis. We refit the final models with the new standardized variables plus sex and used the betas from this analysis for comparison between predictors.
Next, we used an independent dataset (N = 22) to test the predictive ability of the peak anterior ground reaction force and step length models. We calculated predicted values for peak anterior ground reaction force and step length using the final models with only fixed-effects terms as the mean of the random term estimates from mixed-effects linear models is approximately zero 50 . We then calculated the R 2 values and the root-mean-square error (RMSE) for the predicted versus actual peak anterior ground reaction force and step length. Because we found that some of the participants in the independent dataset walked with step lengths shorter than those represented in the training data, we also evaluated the R 2 values and the RMSE of the predicted step lengths on a subset of the participants (n = 18) who's actual step lengths were represented in the training dataset.
Finally, to evaluate the performance of our models to the performance of the normative data available we calculated the absolute error for both estimates (|predicted-actual| and |normative-actual|) of peak anterior ground reaction force and step length and compared these values with an unpaired t-test.

Data availability
The training data 30 analyzed in this manuscript are publicly available in the PeerJ repository, https:// peerj. com/ artic les/ 4640/. The independent validation dataset 31 analyzed are available from the corresponding authors of the original manuscript upon reasonable request.